Withdrawing the archers after depleting their ammo is worthy only if you have a reinforcements to bring in. In some cases they are battle winners in long and crippling battles. When all the combat units - either yours and the enemy's are depleted to few men, it is great to have 2 or 4 units of 60 men, even of they are archers. Dont hesitate to use depleted archers to charge enemies if you have nothing else left on the field. This is especially usefull for trebizond archers or bulgarian brigands.

And no - withdrawing is form of organized retreat which do not reduce the morale on the units which are withdrawing nor the morale of other units. Also you can stop the withdrawal at any time by just clicking at ROUT button which is not allways possible if the unit is routing. No matter how many units are withdrawing.

Btw do anyone knows how the bonus for outnumbering 1:2 and 1:3 is calculated? Do they calculate the initial ratio or at every moment of the battle depending of how many troops are on the battlefield or + these in reserve???

And about gaining valor I belive they are gaining it if they deserved it by killing a lot of enemies, no matter do they withdraw or not from the battlefield.